The present invention relates to synthetic array radar (SAR) signal processing, and more particularly, to a phase difference autofocus method for use in such SAR signal processing.
Many real-time SAR radar products require autofocus methods. In an existing phase difference method developed by the assignee of the present invention, an FFT must be done on many range bin of the image. This method is disclosed in U.S. Pat. No. 4,999,635, for "Phase Difference Autofocusing for Synthetic Aperture Radar Imaging," assigned to the assignee of the present invention. One disadvantage of this method is the large number of FFTs required to implement it.
By way of introduction, in the basic phase difference method described in the U.S. Pat. No. 4,999,635, the relative drift between two subimages is estimated without actually forming the subimages. Subarrays are simply mixed and an FFT filter bank is formed from a resulting product. The FFT filters are then detected to form a phase difference autofocus functional. The drift .tau..sub.xy is obtained by finding the location of the peak in the autofocus functional. In order to reduce a statistical noise in estimating the underlying phase errors, this process of forming the autofocus functional is repeated over many range bins. The drift .tau..sub.xy is estimated from the autofocus functional that is integrated over range bins.
The prior art phase difference autofocus method can be summarized in the following steps. A full array from each range bin is divided into two subarrays X, Y. Then, the two subarrays are complex-conjugate multiplied together to produce a cross spectrum of the two sub-maps produced by the subarrays. Next, after amplitude weights have been applied, an FFT is performed on the cross spectrum to produce the complex cross correlation function. One FFT is performed on the subarray complex conjugate product during each range bin processing. If M denotes the length of the subarrays, then each range bin process results in M*log.sub.2 (M) complex multiplies. For simplicity assume an M point FFT is performed. Then, the cross correlation function is magnitude-detected. The magnitude-detected cross correlation function is then summed across range bins to to produce a summed cross correlation function. Next, the location, .tau..sub.xy, of the peak of the summed cross correlation function, which is proportional to the residual quadratic phase error, is found. Finally, the center-to-end quadratic phase phase error, .phi..sub.q, is obtained by multiplying .tau..sub.xy with a conversion factor. To summarize, one FFT operation is required to produce FFT filters for each each range bin. Detected FFT filters are then integrated over range bins. Detection operation is required since those FFT filters can not be coherently added over range bins.
In the cross spectrum derived from the complex-conjugate multiplication step, the predominate frequency is proportional to the residual quadratic phase error found in the original full array. The cross spectrum is not averaged in the prior phase difference method because the initial phase of the predominant frequency is different for each range bin. The magnitude detection of the cross correlation function aligns the data before summation across range bins in this prior phase difference autofocus method.
Accordingly, a more computationally efficient autofocus method is therefore highly desirable for many existing real-time SAR radar products. Since FFTs require extensive computations, a reduction in the number of FFTs substantially reduces the computation time. In real-time systems, minimization of computation time is not only desirable but also essential.